Overcrowding and Hole Probabilities for Random Zeros on Complex Manifolds
نویسنده
چکیده
We give asymptotic large deviations estimates for the volume inside a domain U of the zero set of a random holomorphic section of the N -th power of a positive line bundle on a compact Kähler manifold. In particular, we show that for all δ > 0, the probability that this volume differs by more than δN from its average value is less than exp(−Cδ,UN), for some constant Cδ,U > 0. As a consequence, the “hole probability” that a random section does not vanish in U has an upper bound of the form exp(−CUN).
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تاریخ انتشار 1977